It is known in the field of high-powered lasers that if N individual lasers, each having a single output and sufficient self-feedback (SFB) to sustain lasing action, are each focused on a distant target, the peak intensity seen at the target will be equal to N.times.I; where N is the number of lasers and I is the intensity of a single laser. However, if the N lasers are coupled, i.e., phase-locked or running at the same frequency or mode, such that the phase between output beams is a constant, and they are in-phase with each other, the intensity seen at the target will be N.sup.2 .times.I (i.e., the coherent sum).
One way of providing N.sup.2 I output intensity is to use coupled standing wave resonators, as is discussed in U.S. Pat. No. 4,682,339, to Sziklas et al., entitled "Laser Array Having Mutually Coupled Resonators". In that case, each individual standing wave resonator has a bi-directional optical coupling signal going from one laser to the next, i.e., mutual feedback (MFB). However, to maintain phase lock, the cavity length of each laser must be kept to within approximately .+-. .lambda./20, of an integer multiple of a wavelength of each other (depending on the number of lasers and type of coupling used). It is difficult to achieve this level of cavity length matching due to vibration and thermal effects and because it requires controlling large, e.g., 1 foot in diameter, water-cooled mirrors for high-power lasers.
Another way of achieving N.sup.2 I output intensity at a distant target is to use one large laser cavity (i.e., not individual lasers), such as a folded cavity, and tap-off output beams at various different locations in the cavity. Such a laser is called a Multiple Output Resonator (laser) or MOR, as is known. The advantage of using an MOR is that minor changes in the main resonator cavity length do not affect the coherence (or phaseability; discussed hereinafter) of the output beams because they are inherently coupled by being part of the same cavity.
In a typical MOR, the output beams are tapped-off from physically different locations in the MOR cavity, and the MOR (like most lasers) lases at a plurality of optical frequencies or axial (or longitudinal) modes spaced in frequency by the well known equation c/2L, where c is the speed of light, and L it the total length of the entire MOR cavity. The MOR may also be viewed as a number (N) of "modules", or "elements", i.e., symmetric cavities that make-up the larger MOR cavity. Thus, N modules in an MOR is analogous to N coupled standing wave resonators.
For a symmetrically configured MOR with two modules and, thus, two output beams, output scraper mirrors are positioned such that for a given frequency (or mode), and odd multiples of c/2L therefrom (called "odd modes" herein), the output beams are 180 degrees out of phase with each other. Similarly, in a symmetric MOR, the output beams are physically spaced such that at frequencies equal to the even multiples of c/2L (called "even modes" herein) from the same given frequency the output beams are in-phase with each other. Thus, although the spectral content of each output beam is identical (i.e., same frequency spacing and power output), the phase distribution for each spectral line is not identical. In general, this spectral phase mismatch renders the output beams "unphaseable".
More specifically, for a two-module, dual output beam MOR, the adjacent axial modes of the combined output beams are either in-phase (i.e., even modes) or 180 degrees out of phase (i.e., odd modes). Consequently, simultaneous operation of the MOR laser on adjacent axial modes precludes coherent superposition of the two output beams. Therefore, when the beams are interfered at the target, the even modes form an interference pattern with a peak (or node) in the center, and the odd modes form a pattern with a null (or anti-node) in the center. Thus, when the two intensities are combined the resultant peak intensity seen at the target is NI, not the desired N.sup.2 I.
One way to restore phaseability to the output beams of the MOR is to add cumbersome external delay lines, one for each output, to make it appear as though the output beams are being tapped-off from the same location in the cavity.
It is known that the characteristic equation (or denominator of the transfer function) of a laser system typically has complex roots (or eigenvalues) one corresponding to each mode (i.e., each resonating/lasing optical frequency). It is also known that the magnitude of each eigenvalue provides an indication of the optical loss (or feedback loss) per pass around the laser cavity for a given mode. The greater the magnitude of the eigenvalue, the lower the feedback loss. Also, the phase of each eigenvalue provides an indication of the actual lasing frequency or mode.
For a small number of coupling lasers (e.g., less than four), the phaseability problem of the MOR does not exist for coupled standing wave resonators. The act of coupling not only serves to phase-lock (i.e., frequency-lock) the lasers, but also makes the system operate on a single set of "supermodes" (different than the modes of an individual standing wave laser). Also, the coupling modifies the mode spectrum from a single standing wave resonator such that one set of supermodes has less loss (i.e., greater eigenvalue magnitude) than all others; thus, the laser system will only lase at those supermodes (frequencies). Further, each member of a supermode set has the same output phase distribution. Thus, for a system with less than four lasers the lasers will naturally lase on a dominant supermode set that ensures all the beams will be in-phase with each other for all the adjacent supermodes in the lasing supermode set.
However, in order to maintain a constant acceptable eigenvalue magnitude (or loss) difference for coupled resonators with more than four coupled lasers, each laser must be coupled to every other laser in the system, typically called "tight" coupling. Such a coupling configuration gets quite complex and cumbersome for a large number of lasers because of the high number of interconnects between lasers. This is especially true for high power, physically large lasers, e.g., lasers that are about 20 feet long.
If a coupling configuration other than tight coupling is used for coupled resonators, such as "series" coupling (where each laser is only coupled to adjacent lasers in the system), the eigenvalue magnitude difference decreases (like 1/N.sup.2) as the number N of lasers increases. Thus, as the number of lasers increases, it becomes more difficult to distinguish between one mode and another, and the system will begin to lase at modes that cause phaseability problems.
In the case of the MOR, the eigenvalues are all the same magnitude for any number of lasers. Thus, the eigenvalue magnitude difference is essentially zero and the MOR will lase at both the even and the odd modes (discussed hereinbefore).
Therefore, it is desirable to achieve a coupled laser system having a large number of lasers (e.g., greater than four) that provides the N.sup.2 I intensity effect, that is not highly sensitive to cavity length variations and does not require precise control of cavity lengths. Also, it is desirable to have a system that has an acceptable eigenvalue magnitude (or loss) difference which allows the laser to lase only at the desired modes and has an loss difference that remains substantially constant (or above a desired threshold) as the number of lasers is increased, thereby providing a "scalable" laser system, i.e., a laser system that may be scaled to any number of lasers while maintaining the desired N.sup.2 I intensity scaling of the coherent sum.